Question: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}5x+3y &= -7 \\ 2x+y &= -5\end{align*}$
Answer: Begin by moving the $x$ -term in the second equation to the right side of the equation. $y = {-2x-5}$ Substitute this expression for $y$ in the first equation. $5x+3({-2x - 5}) = -7$ $5x - 6x - 15 = -7$ Simplify by combining terms, then solve for $x$ $-1x - 15 = -7$ $-1x = 8$ $x = -8$ Substitute $-8$ for $x$ back into the top equation. $5( -8)+3y = -7$ $-40+3y = -7$ $3y = 33$ $y = 11$ The solution is $\enspace x = -8, \enspace y = 11$.